Computing Linear Systems on Metric Graphs

Algebra Seminar
Monday, January 25, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
UC Berkeley
A Linear system on metric graphs is a set of effective divisors.  It has the structure of a cell complex. We introduce the anchor divisors in it - they serve as the landmarks for us to compute the f-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex hull of rational functions. We can also compute the extremal generators of the tropical convex hull using the landmarks. We apply these methods to some examples - $K_{4}$ and $K_{3,3}$..